Method and system for reduction of peak-to-average power ratio of transmission signals comprising overlapping waveforms

ABSTRACT

The present invention provides a method and system for reducing the peak to average power ratio (PAP) of a signal with low computational complexity. According to one embodiment, the present invention is applied to reduce the PAP of an OFDM signal. According to an alternative embodiment, the present invention, is applied to reduce the PAP of a CDMA signal. Rather than seeking the optimum solution, which involves significant computational complexity, the present invention provides for a number of sub-optimal techniques for reducing the PAP of an OFDM signal but with much lower computational complexity. In particular, according to one embodiment utilizing the PTS approach, an iterative technique is used to assign phase factors to each of a set of partial transmit sequences from a set of possible phase factors. Experimental results using the iterative technique showed only a slight degradation (1 dB) from the optimal approach using the same number of subblocks and subcarriers. In an alternative embodiment, which avoids feedback required by the iterative approach, a sequence of phase factors are generated randomly and assigned to each of a set of partial transmit sequences. This procedure is repeated for a pre-determined number of trials and the random sequence generating the lowest PAP is selected. In a third embodiment, a set of phase factors is generated using a structured sequence such as a Walsh sequence.

FIELD OF THE INVENTION

This application is a continuation of U.S. patent application Ser. No.10/358,257 filed Feb. 5, 2003, currently allowed, which is acontinuation of U.S. patent application Ser. No. 09/324,487 filed Jun.2, 1999, entitled “Method and System for Reducing of Peak-to-AveragePower Ratio of Transmission Signals Comprising Overlapping Waveforms”(now U.S. Pat. No. 6,556,557). Both of the aforementioned applicationsare herein incorporated by reference in their entirety.

The present invention relates to communication networks. In particularthe present invention relates to a method and system for reducing thepeak to average power ratio of wireless signals.

BACKGROUND INFORMATION

It is predicted that the 21st century will witness the widespreaddeployment of wireless networks that will revolutionize the concept ofcommunication and information processing for business, professional andprivate applications. However, bandwidth scarcity and a hostile radioenvironment are among the two most significant technical hurdles fordeveloping the next generation of wireless information systems. Thelatter issue is especially problematic in developing broadband wirelessnetworks.

In particular, multipath delay spread resulting in intersymbolinterference imposes an absolute limit on the bandwidth of a wirelesschannel. Orthogonal frequency division multiplexing (OFDM) is a veryattractive technique for achieving high-bit-rate transmission in a radioenvironment. By dividing the total bandwidth into many narrowsubchannels, each carrying a lower bit rate, which are transmitted inparallel, the effects of multipath delay spread can be minimized. Thus,the problem of intersymbol interference can be solved by increasing thesymbol duration in the same ratio as the number of subchannels. Thisapproach has been proposed or adopted for many wireless applicationsincluding digital audio broadcasting, digital terrestrial televisionbroadcasting, wireless LANs and high-speed cellular data. Techniques forimplementing OFDM are well known.

However, a significant disadvantage of employing OFDM for wirelessapplications is the potentially large peak-to-average power ratio (PAP)characteristic of a multi carrier signal with a large number ofsubchannels. In particular, a baseband OFDM signal with N subchannelshas a PAP of N²/N=N, for N=256, PAP=24 dB. When passed through anonlinear device, such as a transmit power amplifier, the signal maysuffer significant spectral spreading and in-band distortion. With theincreased interest in OFDM for wireless applications, reducing the PAPis a necessity for implementing OFDM.

For wireless applications, efficient power amplification is required toprovide adequate area coverage and to minimize battery consumption. Theconventional solution to the PAP problem in OFDM systems is to use alinear amplifier that is operated with large backoff from its peak powerlimit. However, this approach results in a significant power penalty.

Several alternative solutions have been proposed to reduce the PAP. Forexample, one simple solution is to deliberately clip the OFDM signalbefore amplification, which provides a good PAP but at the expense ofperformance degradation. See R. O'Neill and L. N. Lopes, “EnvelopeVariations and Spectral Splatter in Clipped Multicarrier Signals,” Proc.of PIMRC'99, pp. 71-75.

Another known conventional solution is nonlinear block coding, where thedesired data sequence is embedded in a larger sequence and only a subsetof all possible sequences are used, specifically those with low peakpowers. See A. E. Jones, T. A. Wilkinson, and S. K. Barton, “BlockCoding Scheme for Reduction of Peak to Mean Envelope Power Ratio ofMulticarrier Transmission Scheme,” Electron. Letts., Vol. 30, No. 25,December 1994, pp. 2098-2099. Using this nonlinear block codingapproach, a 3-dB PAP can be achieved with only a small bandwidthpenalty. However, the drawback of nonlinear block coding is that itrequires large look-up tables at both the transmitter and receiver,limiting its usefulness to applications with only a small number ofsubchannels. There has been progress in developing coding schemes thatreduce the PAP, can be implemented in systematic form, and have someerror correcting capabilities. See A. E. Jones and T. A. Wilkinson,“Combined Coding for Error Control and Increased Robustness to SystemNonlinearities in OFDM,” Proc. of VTC'96, pp. 904-908. Nevertheless,these coding methods are difficult to extend to systems with more than afew subchannels and the coding gains are small for reasonable levels ofredundancy.

Two promising techniques for improving the statistics of the PAP of anOFDM signal have been proposed. These techniques have been termed theselective mapping (SLM) approach and the partial transmit sequence (PTS)approach.

In selective mapping, M statistically independent sequences aregenerated from the same information and that sequence with the lowestPAP is chosen for transmission. To recover the data, the receiver must“know” which sequence has been used to “multiply” the data; this can betransmitted as side information.

In the PTS approach, each input data block consisting of a set ofsubcarrier coefficients is partitioned into disjoint subblocks, whichare then combined to minimize the PAP. Specifically, each subcarriercoefficient is multiplied by a weighting coefficient, or phase factor.The phase factors are chosen to minimize the PAP of the transmittedsignal.

Although both the selective mapping approach and the partial transmitsequence approach are useful for improving the statistics of the PAP ofan OFDM signal, both introduce additional implementation complexity. Inparticular the SLM approach requires the use of M full-length (i.e.,N-point) IFFTs (Inverse Fast Fourier Transforms) at the transmitter. ThePTS approach requires a similar number of IFFT's and in additionintroduces additional complexity due to the requirement of optimizingthe assignment of phase factors to each partial transmit sequence. Thiscomputational complexity imposes limitations on battery life,particularly in the terminal unit. Thus, there is a need for a method toreduce the PAP of a signal that can be performed with low computationalcomplexity.

Code Division Multiple Access (CDMA) is another very attractivetechnique for overcoming the bit rate limitations of the multi pathchannel. In addition, one of the approaches for achieving higher (aswell as variable) bit rates consists of individual terminalstransmitting multiple CDMA codes (multi-code CDMA). In both basic CDMAand multi-code CDMA, a similar PAP problem exists and a method forreducing the PAP of such a signal is desirable.

SUMMARY OF THE INVENTION

The present invention provides a method and system for reducing the PAPof a signal with low complexity compared to existing techniques.According to one embodiment, the present invention is applied to reducethe PAP of an OFDM signal. In an alternative embodiment, the presentinvention is applied to reduce the PAP of a CDMA signal. Rather thanseeking the optimum solution, which involves significant computationalcomplexity, the present invention provides for a number of sub-optimaltechniques for reducing the PAP of an OFDM signal but with much lowercomputational complexity. In particular, according to one embodimentutilizing the PTS approach, an iterative technique is used to assignphase factors to each of a set of partial transmit sequences from a setof possible phase factors. Experimental results using the iterativetechnique showed only a slight degradation (1 dB) from the optimalapproach using the same number of subblocks and subcarriers. In analternative embodiment, which avoids feedback required by the iterativeapproach, a sequence of phase factors are generated randomly andassigned to each of a set of partial transmit sequences. This procedureis repeated for a pre-determined number of trials and the randomsequence generating the lowest PAP is selected. In a third embodiment, aset of phase factors is generated using a structured sequence such as aWalsh sequence.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1, which is prior art, is a block diagram that depicts animplementation of OFDM at a wireless transmitter.

FIG. 2, which is prior art, is a block diagram that depicts animplementation of OFDM at a wireless receiver.

FIG. 3 is a graph showing the complementary cumulative distributionfunction (CCDF=PR(PAP>PAP₀) of the PAP of a continuous-time, analog,OFDM signal for the particular case of 256 subcarriers.

FIG. 4, which is prior art, is a block diagram depicting the SLMapproach for reducing the PAP of an OFDM signal.

FIG. 5, which is prior art, is a block diagram depicting the PTSapproach for reducing the PAP of an OFDM signal.

FIG. 6 is a block diagram depicting a wireless network architectureaccording to one embodiment of the present invention.

FIG. 7 is a flowchart depicting the steps of an iterative algorithmutilizing partial transmit sequences for reducing the PAP of an OFDMsignal.

FIG. 8 is a flowchart depicting the steps of an algorithm for reducingthe PAP of an OFDM signal using randomly generated sequences of phasefactors or structured sequences according to one embodiment of thepresent invention.

FIG. 9 shows a comparison of CCDF plots utilizing the iterative approachof the present invention and the optimum approach.

FIG. 10 shows a comparison of CCDF plots for the iterative techniquedemonstrating the effect of varying the number of subblocks.

FIG. 11 shows a comparison of CCDP plots for the iterative techniquedemonstrating the effect of four-phase weighting factors and 16 QAMsignal constellations.

FIG. 12 shows a comparison of CCDP plots for the iterative techniquedemonstrating the effects of the use of power control.

FIG. 13 shows a comparison of CCDP plots for the iterative technique andthe use of random sequences.

FIG. 14 shows a comparison of CCDF plots for the use of iterativetechnique, random sequences and Walsh sequences.

DETAILED DESCRIPTION

The techniques for performing OFDM transmission are well known. In OFDMtransmission, a block of N symbols {X_(n), n=0, 1, . . . N-1} is formedwith each symbol modulating one of a set of N subcarriers {f_(n), n=0,1, . . . N-1}. The N subcarriers are chosen to be orthogonal, i.e.,f_(n)=n Δf, where the subcarrier spacing Δf=1/NT and where T is theoriginal data symbol period. The original signal after digital-to-analogconversion can be expressed as:

$\begin{matrix}{{{x(t)} = {\sum\limits_{n = 0}^{N - 1}{X_{n}^{2\; \pi \; f_{n^{1}}}}}},{0 \leq t \leq {NT}}} & (1)\end{matrix}$

An important advantage of OFDM is that, in sampled form equation (1) canbe implemented using an Inverse Fast Fourier Transform (IFFT).

FIG. 1, which is prior art, is a block diagram that depicts animplementation of OFDM at a wireless transmitter. A block oftransmission data (corresponding to a particular symbol interval u) isdigitally modulated in modulation block 110 using an appropriatemodulation scheme such as quadrature amplitude modulation (QAM). A datavector output from modulation block 110 a d_(u)={d_(u,0), . . . ,d_(u,N-1)} is then mapped onto f_(N) carriers (140 a, 140 b, etc.) via aserial to parallel converter block 120 to form a modulated sub carriercarrier vector X_(u)={X_(u,0), . . . , Xu_(N-1)}. The subcarrier vectorX_(u) comprising all carrier amplitudes associated with OFDM symbolinterval u is transformed into the time domain, using an N-point IDFT(Inverse Discrete Fourier Transform) (150) or IFFT producing time domainvector x_(u). After digital to analog conversion (in D/A converter block155), the continuous time signal x(t) (157) is transmitted over awireless channel via RF block 160 a.

FIG. 2, which is prior art, is a block diagram that depicts animplementation of OFDM at a wireless receiver. A continuous time signalx(t) (157) is received via RF block 160 b. The analog signal isconverted to a digital signal via A/D converter 220 producing timedomain vector x_(u). The time domain vector x_(u) is transformed to thefrequency domain using an N-point DFT (Discrete Fourier Transform) (230)or FFT (Fast Fourier Transform), producing subcarrier vector X_(u).After parallel to serial conversion in block 235, the signal isdemodulated in QAM block 110 b and the transmitted data recovered.

FIG. 3 is a graph showing the complementary cumulative distributionfunction (CCDF=PR(PAP>PAP₀)) of the PAP of continuous-time, analog, OFDMsignal for the particular case of 256 subcarriers. The PAP of atransmitted signal is defined as:

$\begin{matrix}{{PAP} = \frac{\max {{x(t)}}^{2}}{E\lbrack {x(t)}^{2} \rbrack}} & (2)\end{matrix}$

To more accurately approximate the true PAP, the results of FIG. 3 werecomputed by oversampling (1) by a factor of four (e.g., by zero-paddingthe data input to the IFFT).

FIG. 4, which is prior art, is a block diagram depicting the SLMapproach for reducing the PAP of an OFDM signal. Subcarrier vectorX_(u.is) multiplied by M random sequences r₁-r_(M) (420). Eachmultiplied vector is transformed to a time domain vector using an IFFT(430). The PAP of each time domain vector x_(u,1)-x_(u,M.) is calculatedand the sequence with the lowest PAP is selected for transmission (440).

FIG. 5, which is prior art, is a block diagram depicting the PTSapproach for reducing the PAP of an OFDM signal. Subcarrier vector X_(u)is partitioned in M subblocks (510). Each of the M subblocks istransformed to a partial transmit sequence x_(u,1)-x_(u,M) using an IFFT(530). A peak value optimization is then performed on the set of partialtransmit sequences by appropriately assigning to each partial transmitsequence an appropriate phase factor b so that the PAP of the combinedset of partial transmit sequences, each multiplied by its assigned phasefactor 540, is minimized (550). The set of optimized phase factors isobtained by:

$\{ {{\overset{\sim}{b}}_{u}^{(1)},\ldots \mspace{14mu},{\overset{\sim}{b}}_{u}^{(M)}} \} = {\underset{\{{{\overset{\sim}{b}}_{u}^{(1)},\; \ldots \;,{\overset{\sim}{b}}_{u}^{(M)}}\}}{\arg \; \min}( {\max\limits_{0 \leq k < N}{\sum\limits_{m = 1}^{M}{{b_{u}^{m} \cdot x_{u,k}^{(m)}}}}} )}$

The partial transmit sequences, each multiplied by its assigned phasefactor, are linearly combined 560 and transmitted.

In order to reconstruct the signal at the receiver, the receiver musthave knowledge regarding the generation process of the transmitted OFDMsignal (i.e., the chosen set of phase factors). The phase factors,therefore, are transmitted as side information resulting in some loss ofefficiency. Alternatively, differential encoding can be employed acrossthe subcarriers within a subblock; in this case, the overhead is asingle subcarrier per subblock. Using 128 subcarriers with foursubblocks and phase factors limited to the set {±1, ±j}, the 1% PAP canbe reduced by more than 3 dB.

While the SLM and PTS approaches provide significantly improved PAPstatistics for an OFDM transmit signal with little cost in efficiency, asignificant issue in implementing these approaches is reducing thecomputational complexity. In particular, the SLM approach requires theuse of M full-length (i.e., N-point) IFFTs at the transmitter. While thePTS approach requires a similar number of N-point IFFTs (one IFFT foreach partial transmit sequence), computation complexity in computingthese IFFTs is reduced by taking advantage of the fact that a largefraction of the input values are zero (in particular, only N/M valuesare non-zero). Nevertheless, in the PTS approach, an optimization isrequired at the transmitter in order to determine the best combinationof the partial transmit sequences. In its most direct form, this processrequires the PAP to be computed at every step of the optimizationalgorithm, necessitating numerous trials to achieve the optimum. It isknown from C. Tellambura, “Phase Optimisation Criterion for ReducingPeak-to-Average Power Ratio in OFDM,” Electron. Letts., Vol. 34, No. 2,January 1998, pp. 169-170, that using an alternative performancecriterion, less computations are necessary for each trial of theoptimization algorithm.

FIG. 6 is a block diagram depicting a wireless network architecturespecifically adapted to reduce the PAP of signals transmitted throughthe network according to one embodiment of the present invention. Thenetwork depicted in FIG. 6 may be specifically adapted for thetransmission of OFDM signals. In particular, transmitter 105 containsCPU/DSP 110 a, which is specifically adapted either through specifichardware design or software components to perform operations upondigital (discrete time) signals to be transmitted through the wirelessnetwork. CPU/DSP 110 a may also be an ASIC (Application SpecificIntegrated Circuit Device) specifically adapted to perform OFDM as wellas other operations to reduce the PAP of an OFDM signal.

CPU/DSP 110 a communicates with memory 120 a in order to store data andprogram instructions. For example, CPU/DSP 110 a may communicate withmemory 120 a to temporarily store intermediate results of DSP operationson signals to be transmitted through the wireless network. Transmitter105 also contains digital to analog converter 115 for conversion ofdigital signals for wireless transmission to receiver via transponder130 a and antenna 140 a.

Receiver 145 receives wireless signals via antenna 140 b and transponder130 b. Analog signals received at receiver 145 are converted to digitalformat via analog to digital converter 155. Receiver 145 containsCPU/DSP 110 b and memory 120 b for performing operations on receiveddigital signals. In particular, according to one embodiment, CPU/DSP 110b is specifically adapted to perform demultiplexing of OFDM signals aswell as other operations to reconstruct the original signals sent bytransmitter 105.

In the PTS approach, a major portion of the computational complexityoriginates from the need to optimize the phase factors used forcombining the subblocks. FIG. 7 is a flowchart depicting the steps of asub-optimal iterative process for reducing the PAP of an OFDM signal.The procedure is initiated in step 710. In step 720 a set of partialtransmit sequences are generated for a particular signal interval u. Forexample, this may be accomplished by segmenting a subcarrier vectorX_(u) into M subblocks. Then an IFFT is performed on each subblock toproduce each partial transmit sequence. In step 730 an initial phasefactor b_(m) from a set of possible phase factors is assigned to eachpartial transmit sequence. In step 740 the PAP value of a linearcombination of the partial transmit sequences, each multiplied by itsrespective phase factor, is calculated and stored in memory 120 a.

In step 745 each partial transmit sequence is analyzed and assigned afinal phase factor according to steps 750-765. In particular, in step750 the current phase factor assigned to the partial transmit sequenceunder consideration is stored in memory. Then a phase factor from theset of possible phase factors is assigned to the current partialtransmit. The PAP value of the linear combination of the partialtransmit sequences each multiplied by its respective phase factor isthen calculated. In step 755, this calculated PAP value is compared withthe PAP value stored in memory. If the calculated PAP value is lowerthan the PAP value stored in memory (‘yes’ branch of step 755), thecurrent PAP value is stored (step 760) and the partial transmit sequenceunder consideration retains the assigned phase factor. Otherwise, if thecurrent PAP value is greater than the stored PAP value (‘no’ branch ofstep 755), the temporarily stored phase factor from step 750 isre-assigned to the current partial transmit sequence (step 765). In step770, it is determined whether all phase factors from the set of possiblephase factors have been examined for the current partial transmitsequence. If not, (‘no’ branch of step 770), step 750 is executed again.If all phase factors have been examined (‘yes’ branch of step 770), instep 775 it is determined whether all partial transmit sequences havebeen examined and assigned a final phase factor. If not (‘no’ branch ofstep 775), step 745 is executed again. If all partial transmit sequenceshave been examined and assigned a final phase factor, the procedure ends(step 780).

The following pseudo-code defines an embodiment of the presentinvention:

Steps: #define SIZE_OF_PARTIAL_TRANSMIT_SEQUENCE 5 #defineNUMBER_OF_PHASE_FACTORS 2 int phase_factors[2]= {−1,1}; int best_PAP;Struct PTS { int[SIZE_OF_PARTIAL_TRANSMIT_SEQUENCE]; int phase_factor; }{ assign initial phase factor to each partial transmit sequence;best_PAP=PAP of combine set of partial transmit sequences eachmultiplied by its corresponding phase factor; for each partial transmitsequence do{  for (i=0;i<=NUMBER_OF_PHASE_FACTORS-1; i++)  { temp_phase_factor=partial_transmit_sequence.phase_factor; partial_transmit_sequence.phase_factor=phase_factors[i]; current_PAP=PAP of combined set of partial transmit sequences eachmultiplied by its corresponding phase factor;  if current_PAP<best_PAP best_PAP=current_PAP;  else partial_transmit_sequence.phase_factor=temp_phase_factor; }

According to one embodiment of the present invention, the set ofpossible phase factors can take on only binary values from the set {1,−1}. Using this example, after dividing the input data block into Msubblocks, M N-point PTSs are generated using an IFFT. Each partialtransmit sequence is assigned the same phase factor, (i.e., b_(m)=1 forall m). The PAP of the combined signal is then computed. The first phasefactor b₁ is then inverted and the PAP is then recomputed. If the newPAP is lower than in the previous step, b₁ is retained as part of thefinal phase sequence. Otherwise b₁ is reassigned its previous value.This procedure continues in a sequential fashion until all of the Mpossibilities for “flipping” the signs of the phase factors have beenexplored.

Results of the sub-optimal iterative approach (as discussed below) showa significant improvement in the PAP of an OFDM signal with only a smalldegradation compared to the optimum. Nevertheless, the iterativeapproach requires some feedback for implementation. An alternativeapproach, which avoids feedback, is to approximate the optimum by simplymultiplying the desired information sequence by a number of randomsequences and choosing the best to transmit.

FIG. 8 is a flowchart depicting the steps of a sub-optimal techniqueusing random sequences of random phase factors for reducing the PAP ofan OFDM signal according to one embodiment of the present invention. Instep 810 the procedure is initiated. In step 820, for the symbolinterval u, a set of partial transmit sequences is generated (i.e., seediscussion of step 720 in FIG. 7). In step 830 a PAP value of a linearcombination of the partial transmit sequences is calculated and storedin memory 120 a. In step 840, a vector of random phase factors r isgenerated. In step 850, the PAP value of the combined partial transmitsequences each multiplied by a corresponding phase factor in r iscalculated. If the PAP value using the current vector r is lower thanthe stored PAP value (‘yes’ branch of step 855), the vector r and thecurrent PAP value are stored (step 860). Otherwise (‘no’ branch of step855), it is determined whether a sufficient number of random sequenceshave been considered (i.e., the number of random sequences is userdetermined). If a pre-determined number of sequences have not beenconsidered (‘no’ branch of step 865), step 840 is executed again andanother random vector is generated. Otherwise, the procedure ends instep 870 and the currently stored vector r is used for transmission.

According to simulation results (discussed in more detail below), it wasfound that 16 random trials produced statistically the same results asthe iterative approach described above. Based upon this observation,according to an alternative embodiment of the present invention, a knownset of sequences, which are easily generated, were used instead ofrandom sequences. According to one embodiment, for example, Walshsequences were used. Walsh functions reduce the number of requiredadditions by a large factor if partial sums are stored. This is similarto the way a FFT reduces the computations required for a DFT. Usingstructured sequences such as Walsh sequences resulted in degradation ofonly 0.3 dB. Similar results can be obtained with other well-knownsequences such as the Shapiro-Rudin sequences.

Simulation Parameters

The PAP is associated with the continuous-time OFDM transmit signal.Many experimental results compute the PAP based on T or symbol-sampleddata in which case overly-optimistic results are produced due to missingpeaks in the signal. Simulations, with regard to the present invention,were conducted in which the transmitted symbol was oversampled by afactor of four. Simulations showed that this oversampling was sufficientto capture signal peaks. In the results, described below, 100000 randomOFDM blocks were generated to obtain CCDF plots. 256 subcarriers wereused as were QPSK data symbols.

Simulation Results

FIG. 9 shows a comparison of CCDF plots utilizing the iterative approachof the present invention and the optimum approach for the case of asingle OFDM block and 16 subblocks each composed of 16 subcarriers. Theunmodified OFDM signal exhibits a PAP which exceeds 10.4 dB for lessthan 1% of the blocks. By using the PTS approach with the optimum binaryphase sequence for combining, the 1% PAP can be reduced to 6.8 dB. Inaddition, the slope is improved so that the reduction in the PAP wouldbe even more significant at lower values of the CCDF. Using theiterative technique, a value of 7.8 dB was obtained. While thisrepresents a degradation of 1 dB, the optimization process is reduced to16 set of 16 additions, a considerable savings over attempting to findthe optimum set of phase factors (the PAP is actually computed 17 times,including the case where b_(m)=1 for all m).

FIG. 10 shows CCDF plots for the iterative technique demonstrating theeffect of varying the number of subblocks. FIG. 10 shows CCDF plotsusing the iterative technique for 4, 8 and 16 subblocks, each increasein the number of subblocks impacting the complexity of theimplementation. As expected, the improvement decreases as the number ofsubblocks decreases. However, FIG. 10 shows that with only 8 subbocks,and therefore, only 8 additional steps in the optimization, a reductionof more than 2 dB in the 1% PAP was achieved.

FIG. 11 shows CCDF plots for the iterative technique demonstrating theeffects of allowing the phase factors to be chosen from the set {±1, ±j}instead of the binary set {−1, 1}. As shown in FIG. 11, for 16 subblocksthe effect is small. With only 16 steps, the additional degrees offreedom were not enough to offset the increased possibility ofencountering a poor sequence. For a smaller number of subblocks, theadded degree of freedom in choosing the phase factors provided only anaddition 0.4 dB reduction. Also, the results showed that using a 16-QAMconstellation to modulate each subcarrier resulted in negligibledifferences from the QPSK (Quadrature Phase Shift Keying) case.

OFDM has been proposed for use in many applications, includingmultiple-user or multiple-access modes. For such an application, thebase station transmits a block of N subchannels in which only a smallsubset of the subchannels are intended for an individual mobile orportable receiver. In this case, the signals to be transmitted (e.g., 16subcarriers for each of the 16 users) are combined and transmitted overone antenna at the base station. However, each of the user-clusters istransmitted with a different power level, usually depending on thedistance from the base to the individual portable receiver. Given theuse of power control, it is necessary to assess its effect on the PAPwhen the iterative technique is used.

FIG. 12 shows CCDF plots for the iterative technique demonstrating theeffect of no power control, power control with the transmit levelschosen uniformly in the interval [−10 dB, 0 dB] and power control inwhich the transmit levels are chosen from a distribution with a widerspread [−20 dB, 0 dB]. As shown from the plots of FIG. 12, theadditional variations in transmitter power in each subblock resulted invery little degradation for the 10-dB spread case and about 0.5 dB forthe 20 dB case. These results depict a worst-case scenario. In morerealistic scenarios the distribution would not be uniform and thedegradation would be minimal.

FIG. 13 shows a comparison of CCDF plots for the iterative technique andthe use of random sequences. FIG. 13 shows results using 5, 16, 200 and2000 random phase sequences (each of length M). Note that 2000 triesresults in performance, which is essentially equal to the globaloptimum. However, even using as few as 5 random tries, it is possible toobtain results within 1.5 dB of the optimum.

FIG. 14 shows a comparison of CCDF plots for the use of iterativetechnique, random sequences and Walsh sequences. FIG. 14 shows resultswhen the 16 Walsh sequences of length 16 are used. These sequencesresult in a degradation of only 0.03 dB.

1. A method for reducing a peak to average power ratio (PAP) of a signalcomprising: assigning a phase factor to each of a plurality of vectors;calculating a first PAP value of a combined signal comprising a linearcombination of each of the plurality of vectors multiplied by acorresponding phase factor assigned to each of said of the plurality ofvectors; and assigning a final phase factor to each of said plurality ofvectors, wherein the final phase factor is assigned on a basis that aPAP of the combined signal will be minimized.
 2. The method of claim 1,wherein the signal is an orthogonal frequency division multiplexed(OFDM) signal.
 3. The method of claim 1, wherein the signal is awireless signal transmitted using code division multiple access (CDMA).4. The method of claim 1, wherein the signal is a wireless signaltransmitted using multicode CDMA.
 5. The method of claim 1, wherein theplurality of vectors comprises partial transmit sequences.
 6. A wirelesstransmitter, comprising: a transponder device; a memory; and a processorcoupled to said memory and said transponder device, said processoradapted to: assign a phase factor to each of a plurality of vectors;calculate a first PAP value of a combined signal comprising a linearcombination of each of the plurality of vectors multiplied by acorresponding phase factor assigned to each of said of the plurality ofvectors; and assign a final phase factor to each of said plurality ofvectors, wherein the final phase factor is assigned on a basis that aPAP of the combined signal will be minimized.
 7. The wirelesstransmitter of claim 6, wherein the signal is an orthogonal frequencydivision multiplexed (OFDM) signal.
 8. The wireless transmitter of claim6, wherein the signal is a wireless signal transmitted using codedivision multiple access (CDMA).
 9. The wireless transmitter of claim 6,wherein the signal is a wireless signal transmitted using multicodeCDMA.
 10. The wireless transmitter of claim 6, wherein the plurality ofvectors comprises partial transmit sequences.
 11. An apparatus forreducing a peak to average power ratio (PAP) of a signal comprising:means for assigning a phase factor to each of a plurality of vectors;means for calculating a first PAP value of a combined signal comprisinga linear combination of each of the plurality of vectors multiplied by acorresponding phase factor assigned to each of said of the plurality ofvectors; and means for assigning a final phase factor to each of saidplurality of vectors, wherein the final phase factor is assigned on abasis that a PAP of the combined signal will be minimized.
 12. Theapparatus of claim 11, wherein the signal is an orthogonal frequencydivision multiplexed (OFDM) signal.
 13. The apparatus of claim 11,wherein the signal is a wireless signal transmitted using code divisionmultiple access (CDMA).
 14. The apparatus of claim 11, wherein thesignal is a wireless signal transmitted using multicode CDMA.
 15. Theapparatus of claim 11, wherein the plurality of vectors comprisespartial transmit sequences.